We study quarkonium in hot QCD, emphasizing its nature as a. short-lived transient, with ail exponentially decaying wave function. The heavy quark mass allows for a nonrelativistic expansion around the two-quark threshold, and the static potential is then seen to contain a temperature-dependent imaginary part, which leads to ail unstable quark-antiquark state. We solve the corresponding Schrodinger equation and estimate the spectral functions in different channels. In particular, through careful evaluation we Find a, peak also in the scalar channel, although it is Strongly suppressed with respect to the vector channel peak. We also plot the dilepton production rate, which shows a peak-like structure even at temperatures so high that the peak in the spectral function has disappeared.